Analysis of a Polynomial Chaos-Kriging Metamodel for Uncertainty Quantification in Aerospace Applications

Weinmeister, Justin; Xie, Nelson; Gao, Xinfeng; Prasad, Aditi Krishna; Roy, Sourajeet

doi:10.2514/6.2018-0911

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…Chaos phenomenon developed by creating irregular phenomena can be desirable for many applications and undesirable for many other applications [1][2][3][4]. For example, chaotic systems with optimal conditions can be used in secure communications [5], cryptography [6], economics [7], aerospace [8], event-triggered communication [9], masking communication [10], transportation [11], mechanics [12], power systems [13] and other sciences. Chaos theory also has been considered in stochastic systems [14], memristor-based circuits [15], neural systems [16], finite-size systems [17], urban systems [18], quantum systems [19], Takagi-Sugeno (TS) fuzzy systems [20,21], etc.…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

Alattas

Mostafaee

Sambas³

et al. 2021

Mathematics

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In this study, the synchronization problem of chaotic systems using integral-type sliding mode control for a category of hyper-chaotic systems is considered. The proposed control method can be used for an extensive range of identical/non-identical master-slave structures. Then, an integral-type dynamic sliding mode control scheme is planned to synchronize the hyper-chaotic systems. Using the Lyapunov stability theorem, the recommended control procedure guarantees that the master-slave hyper-chaotic systems are synchronized in the existence of uncertainty as quickly as possible. Next, in order to prove the new proposed controller, the master-slave synchronization goal is addressed by using a new six-dimensional hyper-chaotic system. It is exposed that the synchronization errors are completely compensated for by the new control scheme which has a better response compared to a similar controller. The analog electronic circuit of the new hyper-chaotic system using MultiSIM is provided. Finally, all simulation results are provided using MATLAB/Simulink software to confirm the success of the planned control method.

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Section: Introduction 1background and Motivationmentioning

confidence: 99%

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

Alattas

Mostafaee

Sambas³

et al. 2021

Mathematics

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“…Some scholars have optimized the wind turbine blade from the low wind speed 16,17 and the multi-objective. [18][19][20][21] The surrogate model method has been a widely used in the geology, 22 the meteorology, 23 the remote sensing, 24 the aerospace 25 and the wind power. 26 The kriging surrogate model fully considered the distance between the sample points and the aggregation of the sample points, which could well reflect the spatial distribution and continuity of the variables in the process of the valuation.…”

Section: Introductionmentioning

confidence: 99%

Numerical optimization of horizontal-axis wind turbine blades with surrogate model

Wang

Jiang

Chao

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part A:

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Wind energy is a widely used and developed the renewable energy, which has developed rapidly. At present, the design of the horizontal axis wind turbine blade mainly used Blade Element Momentum theory. In this paper, an optimization method of the wind turbine blade was proposed for improving the output power. The local twist angles of the blade were optimized. This method combined the surrogate model and the numerical simulation methods. The kriging surrogate model was selected and the next calibration point was chosen by the efficient global optimization algorithm. In this paper, the aerodynamic performances of the optimized blades were discussed in detail and obtained by the numerical simulation method. It was shown that the wind power coefficients and the output powers of the optimized blades were increased. The wind power coefficients of two optimized blades were increased by 4.83% and 3.44%, respectively. The optimized blades were able to capture more kinetic energy from the wind, but the optimized blades were subjected to a greater structural load. The thrust and torque coefficients maintained an increasing tendency for the optimized blades.

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“…Obviously, this method is expensive since one needs to construct many PCE models in each iteration. Moreover, Schöbi et al investigated the application of PCE‐Kriging model for reliability analysis adaptively, where the most relevant basis functions are firstly selected by the least angle regression technique, and then a Kriging model is trained based on the selected basis functions. This technique combines the advantages of both sparse PCE and Kriging model, but training the PC‐Kriging model is time‐consuming compared to single model.…”

Section: Introductionmentioning

confidence: 99%

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Cheng

Lü

2020

Numerical Meth Engineering

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Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis.This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.

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Analysis of a Polynomial Chaos-Kriging Metamodel for Uncertainty Quantification in Aerospace Applications

Cited by 7 publications

References 15 publications

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

Numerical optimization of horizontal-axis wind turbine blades with surrogate model

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

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